What is the solution for 2(d^2y)/(dx^2)+(dy)/(dx)-105y=0 ?

The solution for 2(d^2y)/(dx^2)+(dy)/(dx)-105y=0 is y=c_{1}e^{7x}+c_{2}e^{-(15x)/2}

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2(d^2y)/(dx^2)+(dy)/(dx)-105y=0

2 \frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} - 105 y = 0

y = c_{1} e^{7 x} + c_{2} e^{- \frac{15 x}{2}}

Solution steps

2 \frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} - 105 y = 0

Solve linear ODE:

y = c_{1} e^{7 x} + c_{2} e^{- \frac{15 x}{2}}

y = c_{1} e^{7 x} + c_{2} e^{- \frac{15 x}{2}}

6 y^{^{''''}} + 77 y^{^{''}} + 255 y = 0

y^{^{''}} - 0.28 y^{^{'}} - 0.006 y = 0

2 \cdot y^{^{''}} + 4 \cdot y^{^{'}} + 8 y = 0, y (0) = 5, y^{^{'}} (0) = 0

4 y^{^{''}} + \frac{16}{0.25} y = 0

5 \frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} - 6 y = 0

What is the solution for 2(d^2y)/(dx^2)+(dy)/(dx)-105y=0 ?
The solution for 2(d^2y)/(dx^2)+(dy)/(dx)-105y=0 is y=c_{1}e^{7x}+c_{2}e^{-(15x)/2}